code: def is_independent(
      func,
      interface,
      args,
      kwargs=None,
      num_pos=5,
      seed=9123,
      atol=1e-6,
      rtol=0,
      bounds=(-np.pi, np.pi),
  ):
      """Test whether a function is independent of its input arguments,
      both numerically and analytically.
  
      Args:
          func (callable): Function to be tested
          interface (str): Autodiff framework used by ``func``. Must correspond to one
              of the supported PennyLane interface strings, such as ``"autograd"``,
              ``"tf"``, ``"torch"``, ``"jax"``.
          args (tuple): Positional arguments with respect to which to test
          kwargs (dict): Keyword arguments for ``func`` at which to test;
              the keyword arguments are kept fixed in this test.
          num_pos (int): Number of random positions to test
          seed (int): Seed for the random number generator
          atol (float): Absolute tolerance for comparing the outputs
          rtol (float): Relative tolerance for comparing the outputs
          bounds (tuple[float]): 2-tuple containing limits of the range from which to sample
  
      Returns:
          bool: Whether ``func`` returns the same output at randomly
          chosen points and is numerically independent of its arguments.
  
      .. warning::
  
          This function is experimental.
          As such, it might yield wrong results and might behave
          slightly differently in distinct autodifferentiation frameworks
          for some edge cases.
          For example, a currently known edge case are piecewise
          functions that use classical control and simultaneously
          return (almost) constant output, such as
  
          .. code-block:: python
  
              def func(x):
                  if abs(x) <1e-5:
                      return x
                  else:
                      return 0. * x
  
      The analytic and numeric tests used are as follows.
  
      - The analytic test performed depends on the provided ``interface``,
        both in its method and its degree of reliability.
  
      - For the numeric test, the function is evaluated at a series of random positions,
        and the outputs numerically compared to verify that the output
        is constant.
  
      .. warning ::
  
          Currently, no analytic test is available for the PyTorch interface.
          When using PyTorch, a warning will be raised and only the
          numeric test is performed.
  
      .. note ::
  
          Due to the structure of ``is_independent``, it is possible that it
          errs on the side of reporting a dependent function to be independent
          (a false positive). However, reporting an independent function to be
          dependent (a false negative) is *highly* unlikely.
  
      **Example**
  
      Consider the (linear) function
  
      .. code-block:: python
  
          def lin(x, weights=None):
              return np.dot(x, weights)
  
      This function clearly depends on ``x``. We may check for this via
  
      .. code-block:: pycon
  
          >>> x = np.array([0.2, 9.1, -3.2], requires_grad=True)
          >>> weights = np.array([1.1, -0.7, 1.8], requires_grad=True)
          >>> qml.math.is_independent(lin, "autograd", (x,), {"weights": weights})
          False
  
      However, the Jacobian will not depend on ``x`` because ``lin`` is a
      linear function:
  
      .. code-block:: pycon
  
          >>> jac = qml.jacobian(lin)
          >>> qml.math.is_independent(jac, "autograd", (x,), {"weights": weights})
          True
  
      Note that a function ``f = lambda x: 0.0 * x`` will be counted as *dependent* on ``x``
      because it does depend on ``x`` *functionally*, even if the value is constant for all ``x``.
      This means that ``is_independent`` is a stronger test than simply verifying functions
      have constant output.
      """
  
      # pylint:disable=too-many-arguments
  
      if not interface in {
          "autograd",
          "jax",
          "tf",
          "torch",
          "tensorflow",
      }:
          raise ValueError(f"Unknown interface: {interface}")
  
      kwargs = kwargs or {}
  
      if interface == "autograd":
          if not _autograd_is_indep_analytic(func, *args, **kwargs):
              return False
  
      if interface == "jax":
          if not _jax_is_indep_analytic(func, *args, **kwargs):
              return False
  
      if interface in ("tf", "tensorflow"):
          if not _tf_is_indep_analytic(func, *args, **kwargs):
              return False
  
      if interface == "torch":
          warnings.warn(
              "The function is_independent is only available numerically for the PyTorch interface. "
              "Make sure that sampling positions and evaluating the function at these positions "
              "is a sufficient test, or change the interface."
          )
  
      return _is_indep_numerical(
          func,
          interface,
          args,
          kwargs,
          num_pos,
          seed,
          atol,
          rtol,
          bounds,
      )
  
file_path: pennylane/pennylane/math/is_independent.py
imports: import warnings
  import numpy
  from autograd.tracer import isbox, new_box, trace_stack
  from autograd.core import VJPNode
  from pennylane import numpy
label_desc: Use image node_id 6 for calling a global function with example usage: is_independent(func, interface, args, kwargs, num_pos, seed, atol, rtol, bounds) and returns: _is_indep_numerical, False, False, False